Sample Question Paper 1 - Math, Class 9 Class 9 Notes | EduRev

Mathematics (Maths) Class 9

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Class 9 : Sample Question Paper 1 - Math, Class 9 Class 9 Notes | EduRev

 Page 1


  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 1 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify : ?? (5 5)(5 5)              
 
2. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?         
   
3. In ? ABC, ?A = 100 ? and AB = AC. Find ? B?   
OR 
Find the angles of an isosceles triangle whose equal angles and the non-equal angles 
are in the ratio 3:4. 
4. The cost of notebook is twice the cost of a pen. Write a linear equation in the two 
variables to represent this statement? 
 
5. Find the range of data: 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, and 35. 
OR 
 What is the class mark of the class interval 45-52? 
 
6. In a parallelogram PQRS, What is the sum of ?R and ?S?  
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify:           
 
??
? ? ? ?
?
? ? ? ?
? ? ? ?
3/ 4 3/2
81 25
16 9
 
OR 
Page 2


  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 1 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify : ?? (5 5)(5 5)              
 
2. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?         
   
3. In ? ABC, ?A = 100 ? and AB = AC. Find ? B?   
OR 
Find the angles of an isosceles triangle whose equal angles and the non-equal angles 
are in the ratio 3:4. 
4. The cost of notebook is twice the cost of a pen. Write a linear equation in the two 
variables to represent this statement? 
 
5. Find the range of data: 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, and 35. 
OR 
 What is the class mark of the class interval 45-52? 
 
6. In a parallelogram PQRS, What is the sum of ?R and ?S?  
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify:           
 
??
? ? ? ?
?
? ? ? ?
? ? ? ?
3/ 4 3/2
81 25
16 9
 
OR 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
Simplify: 
2
2
3
0 81
7
27 3
 
 
8. Factorise:
  
2
2
12
x 2 2x
xx
? ? ? ?
 
 
9. Where do the following points lie?               
a. (–4, 0) 
b. (–10, 2) 
c. (0, 8) 
d. (10, 4) 
 
10. In the given figure, ABCDE is a pentagon. A line through B and parallel to AC meets DC 
produced at F. Show that area(?ACB) = area(?ACF). 
 
 
11. A rectangular metallic sheet has dimensions 48 cm × 36 cm. From each corner a 
square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume 
of the box. 
OR 
 Find the length of the diagonal in the following cases cuboid of 11 cm by 10 cm by 2 
cm. 
12. Find the value of k, if x = 1, y = 1 is a solution of the equation 9kx + 12ky = 63. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Simplify: 
? ? ? ? ?
??
33
25
43 5
35 4
25 343
16 8 7
   
                       
14. (x + 2) is one of the factors of the polynomial x
3
 + 13x
2
 + 32x + 20. Find its remaining 
factors.                
        
 
 
 
 
Page 3


  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 1 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify : ?? (5 5)(5 5)              
 
2. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?         
   
3. In ? ABC, ?A = 100 ? and AB = AC. Find ? B?   
OR 
Find the angles of an isosceles triangle whose equal angles and the non-equal angles 
are in the ratio 3:4. 
4. The cost of notebook is twice the cost of a pen. Write a linear equation in the two 
variables to represent this statement? 
 
5. Find the range of data: 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, and 35. 
OR 
 What is the class mark of the class interval 45-52? 
 
6. In a parallelogram PQRS, What is the sum of ?R and ?S?  
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify:           
 
??
? ? ? ?
?
? ? ? ?
? ? ? ?
3/ 4 3/2
81 25
16 9
 
OR 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
Simplify: 
2
2
3
0 81
7
27 3
 
 
8. Factorise:
  
2
2
12
x 2 2x
xx
? ? ? ?
 
 
9. Where do the following points lie?               
a. (–4, 0) 
b. (–10, 2) 
c. (0, 8) 
d. (10, 4) 
 
10. In the given figure, ABCDE is a pentagon. A line through B and parallel to AC meets DC 
produced at F. Show that area(?ACB) = area(?ACF). 
 
 
11. A rectangular metallic sheet has dimensions 48 cm × 36 cm. From each corner a 
square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume 
of the box. 
OR 
 Find the length of the diagonal in the following cases cuboid of 11 cm by 10 cm by 2 
cm. 
12. Find the value of k, if x = 1, y = 1 is a solution of the equation 9kx + 12ky = 63. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Simplify: 
? ? ? ? ?
??
33
25
43 5
35 4
25 343
16 8 7
   
                       
14. (x + 2) is one of the factors of the polynomial x
3
 + 13x
2
 + 32x + 20. Find its remaining 
factors.                
        
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
15. In the figure, it is given that LM = MN and LP = QN. Prove that ? LMQ ? ? NMP
      
 
 
 
 
 
 
 
 
OR 
The following pairs of triangles are congruent? Give reasons 
 
16. The polynomials p(x) = ax
3
 + 3x
2
 – 3 and q(x) = 2x
3
 – 5x + a when divided by (x – 4) 
leave the remainders R1 and R2. Find ‘a’ if R1 + R2 = 0. Factorise the polynomial. 
 
17. In figure, AB = AC, D is the point in the interior of ? ABC such that ? DBC = ? DCB. 
Prove that AD bisects ? BAC of ? ABC. 
 
 
18. A card is drawn at random from a well-shuffled deck of playing cards. Find the 
probability that the card drawn is a  
(a) queen 
(b) non-ace card 
(c) black card 
 
19. Show that the line segments joining the mid points of the opposite sides of a 
quadrilateral bisect each other.  
OR 
 
Page 4


  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 1 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify : ?? (5 5)(5 5)              
 
2. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?         
   
3. In ? ABC, ?A = 100 ? and AB = AC. Find ? B?   
OR 
Find the angles of an isosceles triangle whose equal angles and the non-equal angles 
are in the ratio 3:4. 
4. The cost of notebook is twice the cost of a pen. Write a linear equation in the two 
variables to represent this statement? 
 
5. Find the range of data: 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, and 35. 
OR 
 What is the class mark of the class interval 45-52? 
 
6. In a parallelogram PQRS, What is the sum of ?R and ?S?  
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify:           
 
??
? ? ? ?
?
? ? ? ?
? ? ? ?
3/ 4 3/2
81 25
16 9
 
OR 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
Simplify: 
2
2
3
0 81
7
27 3
 
 
8. Factorise:
  
2
2
12
x 2 2x
xx
? ? ? ?
 
 
9. Where do the following points lie?               
a. (–4, 0) 
b. (–10, 2) 
c. (0, 8) 
d. (10, 4) 
 
10. In the given figure, ABCDE is a pentagon. A line through B and parallel to AC meets DC 
produced at F. Show that area(?ACB) = area(?ACF). 
 
 
11. A rectangular metallic sheet has dimensions 48 cm × 36 cm. From each corner a 
square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume 
of the box. 
OR 
 Find the length of the diagonal in the following cases cuboid of 11 cm by 10 cm by 2 
cm. 
12. Find the value of k, if x = 1, y = 1 is a solution of the equation 9kx + 12ky = 63. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Simplify: 
? ? ? ? ?
??
33
25
43 5
35 4
25 343
16 8 7
   
                       
14. (x + 2) is one of the factors of the polynomial x
3
 + 13x
2
 + 32x + 20. Find its remaining 
factors.                
        
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
15. In the figure, it is given that LM = MN and LP = QN. Prove that ? LMQ ? ? NMP
      
 
 
 
 
 
 
 
 
OR 
The following pairs of triangles are congruent? Give reasons 
 
16. The polynomials p(x) = ax
3
 + 3x
2
 – 3 and q(x) = 2x
3
 – 5x + a when divided by (x – 4) 
leave the remainders R1 and R2. Find ‘a’ if R1 + R2 = 0. Factorise the polynomial. 
 
17. In figure, AB = AC, D is the point in the interior of ? ABC such that ? DBC = ? DCB. 
Prove that AD bisects ? BAC of ? ABC. 
 
 
18. A card is drawn at random from a well-shuffled deck of playing cards. Find the 
probability that the card drawn is a  
(a) queen 
(b) non-ace card 
(c) black card 
 
19. Show that the line segments joining the mid points of the opposite sides of a 
quadrilateral bisect each other.  
OR 
 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
   Point M and N are taken on the diagonal AC of a parallelogram ABCD such that AM =  
  CN. Prove that BMDN is a parallelogram. 
 
20. In the given figure, ABCD is a cyclic quadrilateral, in which AC and BD are the 
diagonals. If m ?DBC = 55° and m ?BAC = 45°, find m ?BCD. 
 
 
21. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete 
revolutions to move over once to level a playground. Find the area of the playground 
in m
2
? 
22
7
??
??
??
??
 
OR 
 A room is 22 m long, 15 m broad and 6 m high. Find the area of its four walls and the 
cost of painting it including doors and windows at the rate of Rs 12 per m
2
. 
 
22. The following observations have been arranged in the ascending order. 
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95     
If the median of the data is 63, find the value of x.  
OR 
The number of goals scored by Arsenal Football Club in the English Premier League 
in the season 2007 was: 
1, 2, 1, 3, 2, 5, 1, 6, 4, 4, 2, 3, 5, 6, 4, 2, 2, 3, 4, 1, 0, 5, 0, 5, 3, 2, 3, 4, 4, 1, 1, 2, 4, 3, 1, 4 
Arrange these data in a discrete frequency distribution table and answer the 
following: 
(i) What is the range of the number of goals scored by AFC? 
(ii) How many times did AFC score 3 or more than 3 goals? 
(iii) Which variate has the highest frequency? 
 
 
Page 5


  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 1 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify : ?? (5 5)(5 5)              
 
2. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?         
   
3. In ? ABC, ?A = 100 ? and AB = AC. Find ? B?   
OR 
Find the angles of an isosceles triangle whose equal angles and the non-equal angles 
are in the ratio 3:4. 
4. The cost of notebook is twice the cost of a pen. Write a linear equation in the two 
variables to represent this statement? 
 
5. Find the range of data: 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, and 35. 
OR 
 What is the class mark of the class interval 45-52? 
 
6. In a parallelogram PQRS, What is the sum of ?R and ?S?  
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify:           
 
??
? ? ? ?
?
? ? ? ?
? ? ? ?
3/ 4 3/2
81 25
16 9
 
OR 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
Simplify: 
2
2
3
0 81
7
27 3
 
 
8. Factorise:
  
2
2
12
x 2 2x
xx
? ? ? ?
 
 
9. Where do the following points lie?               
a. (–4, 0) 
b. (–10, 2) 
c. (0, 8) 
d. (10, 4) 
 
10. In the given figure, ABCDE is a pentagon. A line through B and parallel to AC meets DC 
produced at F. Show that area(?ACB) = area(?ACF). 
 
 
11. A rectangular metallic sheet has dimensions 48 cm × 36 cm. From each corner a 
square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume 
of the box. 
OR 
 Find the length of the diagonal in the following cases cuboid of 11 cm by 10 cm by 2 
cm. 
12. Find the value of k, if x = 1, y = 1 is a solution of the equation 9kx + 12ky = 63. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Simplify: 
? ? ? ? ?
??
33
25
43 5
35 4
25 343
16 8 7
   
                       
14. (x + 2) is one of the factors of the polynomial x
3
 + 13x
2
 + 32x + 20. Find its remaining 
factors.                
        
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
15. In the figure, it is given that LM = MN and LP = QN. Prove that ? LMQ ? ? NMP
      
 
 
 
 
 
 
 
 
OR 
The following pairs of triangles are congruent? Give reasons 
 
16. The polynomials p(x) = ax
3
 + 3x
2
 – 3 and q(x) = 2x
3
 – 5x + a when divided by (x – 4) 
leave the remainders R1 and R2. Find ‘a’ if R1 + R2 = 0. Factorise the polynomial. 
 
17. In figure, AB = AC, D is the point in the interior of ? ABC such that ? DBC = ? DCB. 
Prove that AD bisects ? BAC of ? ABC. 
 
 
18. A card is drawn at random from a well-shuffled deck of playing cards. Find the 
probability that the card drawn is a  
(a) queen 
(b) non-ace card 
(c) black card 
 
19. Show that the line segments joining the mid points of the opposite sides of a 
quadrilateral bisect each other.  
OR 
 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
   Point M and N are taken on the diagonal AC of a parallelogram ABCD such that AM =  
  CN. Prove that BMDN is a parallelogram. 
 
20. In the given figure, ABCD is a cyclic quadrilateral, in which AC and BD are the 
diagonals. If m ?DBC = 55° and m ?BAC = 45°, find m ?BCD. 
 
 
21. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete 
revolutions to move over once to level a playground. Find the area of the playground 
in m
2
? 
22
7
??
??
??
??
 
OR 
 A room is 22 m long, 15 m broad and 6 m high. Find the area of its four walls and the 
cost of painting it including doors and windows at the rate of Rs 12 per m
2
. 
 
22. The following observations have been arranged in the ascending order. 
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95     
If the median of the data is 63, find the value of x.  
OR 
The number of goals scored by Arsenal Football Club in the English Premier League 
in the season 2007 was: 
1, 2, 1, 3, 2, 5, 1, 6, 4, 4, 2, 3, 5, 6, 4, 2, 2, 3, 4, 1, 0, 5, 0, 5, 3, 2, 3, 4, 4, 1, 1, 2, 4, 3, 1, 4 
Arrange these data in a discrete frequency distribution table and answer the 
following: 
(i) What is the range of the number of goals scored by AFC? 
(ii) How many times did AFC score 3 or more than 3 goals? 
(iii) Which variate has the highest frequency? 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 1 
 
     
Section D 
(Questions 23 to 30 carry 4 marks each) 
 
23. Find the value of:          
  ? ? ? ?
? ? ? ? ?
1 1 1 1 1
3 8 8 7 7 6 6 5 5 2
 
 
24. How does Euclid's fifth postulate imply the existence of parallel lines? Give a 
mathematical proof.  
         
25. Simplify: 
? ? ? ? ? ?
? ? ? ? ? ?
3 3 3
2 2 2 2 2 2
3 3 3
a b b c c a
a b b c c a
? ? ? ? ?
? ? ? ? ?
  
OR 
If 
1
x5
x
; find (i) 
2
2
1
x
x
, (ii) 
4
4
1
x
x
  
26. In the figure, if AC = BC, ?DCA = ?ECB and ?DBC = ?EAC, then prove that BD = AE.      
 
 
 
 
 
 
 
 
27. The volume of a cylinder is 6358 cu. cm and its height is 28 cm. Find its radius and the 
curved surface area.  
OR 
 Find the cost of sinking a tube well 350 m deep, having a diameter of 4 m at the rate of Rs 16 
per m
3 
. Find also the cost of cementing its inner curved surface at Rs 12 per m
2
 
 
28. Construct a triangle having a perimeter of 12.5 cm and angles in the ratio of 3 : 4 : 5. 
 
29. If two intersecting chords of a circle make equal angles with the diameter passing 
through their point of intersection, prove that the chords are equal. 
OR 
AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are 
diameters; (ii) ABCD is a rectangle.  
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